The opposite charges of the atoms hold the atoms together. One atom can have a positive charge while the other can have a negative charge and this causes an electrostatic attraction causing the atoms to stick to each other like glue. For example, two magnets, can only be attracted to each other when one side of the magnet has a "-" while the other magnet on one side has a "+". They are attracted to each other by these varying charges. The same applies to ionic compounds which are held together by the varying charges of the ions.
